Question

Show that the energy of a magnetic dipole m in a magnetic field B is U--m B

Answer 1

showm

Step-by-step explanation:

Consider a dipole having magnetic moment 'm' is placed in magnetic field
`\vec{B}` then the torque exerted by the field on the dipole is

`\tau = m* B`

`\tau=mBsin\alpha`

Now to rotate the dipole in the field to its final position the work required to be done is

`U=\int \tau d\alpha`

`U=\int mBsin\alpha d\alpha`

`U= -mBcos\alpha`

`U=-\vec{m* \vec{B}}`

Minimum energy mB is for the case when m is anti parallel to B.

Minimum energy -mB is for the case when m is parallel to B.